Fundamentals of Electric Circuits
6th Edition
ISBN: 9780078028229
Author: Charles K Alexander, Matthew Sadiku
Publisher: McGraw-Hill Education
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Chapter 15.6, Problem 15PP
To determine
Find the time-varying function
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Consider the circuit where the initial current in the inductor is29 mA and the initial voltage across the capacitor is 50 V. This circuit wasanalyzed using second-order circuit analysis techniques. Usethe Laplace transform method to find v(t) for t≥0.
Use the Laplace transform to find the solution x(t) to the following initial condition differential equations:
d) 2x” − x’ = H(t − 1) − H(t − 2), given x(0) = 0, x’(0) = 0
what is the laplace transform of the given differential equation? y'' - 2y' - 1 = 0 , y (0) = 0 , y' (0) = 1
Chapter 15 Solutions
Fundamentals of Electric Circuits
Ch. 15.2 - Prob. 1PPCh. 15.2 - Prob. 2PPCh. 15.3 - Prob. 3PPCh. 15.3 - Prob. 4PPCh. 15.3 - Prob. 5PPCh. 15.3 - Prob. 6PPCh. 15.3 - Obtain the initial and the final values of...Ch. 15.4 - Prob. 8PPCh. 15.4 - Find f(t) if F(s)=48(s+2)(s+1)(s+3)(s+4)Ch. 15.4 - Obtain g(t) if G(s)=s3+2s+6s(s+1)2(s+3)
Ch. 15.4 - Find g(t) given that G(s)=20(s+1)(s2+4s+13)Ch. 15.5 - Graphically convolve the two functions in Fig....Ch. 15.5 - Given g(t) and f(t) in Fig. 15.20, graphically...Ch. 15.5 - Use convolution to find vo(t) in the circuit of...Ch. 15.6 - Prob. 15PPCh. 15.6 - Prob. 16PPCh. 15 - Prob. 1RQCh. 15 - Prob. 2RQCh. 15 - Prob. 3RQCh. 15 - Prob. 4RQCh. 15 - Prob. 5RQCh. 15 - If F(s) = 1/(s + 2), then f(t) is (a) e2t u(t) (b)...Ch. 15 - Prob. 7RQCh. 15 - Prob. 8RQCh. 15 - Prob. 9RQCh. 15 - Prob. 10RQCh. 15 - Prob. 1PCh. 15 - Prob. 2PCh. 15 - Prob. 3PCh. 15 - Prob. 4PCh. 15 - Prob. 5PCh. 15 - Prob. 6PCh. 15 - Prob. 7PCh. 15 - Prob. 8PCh. 15 - Prob. 9PCh. 15 - Prob. 10PCh. 15 - Find F(s) if: (a) ft=6etcosh2t (b) ft=3te2tsinh4t...Ch. 15 - If g(t) = 4e 2t cos 4t, find G(s).Ch. 15 - Prob. 13PCh. 15 - Prob. 14PCh. 15 - Prob. 15PCh. 15 - Prob. 16PCh. 15 - Prob. 17PCh. 15 - Prob. 18PCh. 15 - Prob. 19PCh. 15 - Prob. 20PCh. 15 - Prob. 21PCh. 15 - Prob. 22PCh. 15 - Prob. 23PCh. 15 - Design a problem to help other students better...Ch. 15 - Let F(s)=18(s+1)(s+2)(s+3) (a) Use the initial and...Ch. 15 - Determine the initial and final values of f(t), if...Ch. 15 - Prob. 27PCh. 15 - Prob. 28PCh. 15 - Prob. 29PCh. 15 - Prob. 30PCh. 15 - Find f(t) for each F(s): (a) 10ss+1s+2s+3 (b)...Ch. 15 - Prob. 32PCh. 15 - Prob. 33PCh. 15 - Prob. 34PCh. 15 - Obtain f(t) for the following transforms: (a)...Ch. 15 - Prob. 36PCh. 15 - Prob. 37PCh. 15 - Prob. 38PCh. 15 - Determine f(t) if: (a)...Ch. 15 - Show that...Ch. 15 - Prob. 41PCh. 15 - Design a problem to help other students better...Ch. 15 - Prob. 43PCh. 15 - Prob. 44PCh. 15 - Given h(t) = 4e2tu(t) and x(t) = (t) 2e 2tu(t),...Ch. 15 - Given the following functions...Ch. 15 - A system has the transfer function...Ch. 15 - Find f(t) using convolution given that: (a)...Ch. 15 - Prob. 49PCh. 15 - Prob. 50PCh. 15 - Given that v(0) = 5 and dv(0)/dt = 10, solve...Ch. 15 - Prob. 52PCh. 15 - Prob. 53PCh. 15 - Design a problem to help other students better...Ch. 15 - Prob. 55PCh. 15 - Solve for v(t) in the integrodifferential equation...Ch. 15 - Prob. 57PCh. 15 - Given that dvdt+2v+50tv()d=4u(t) with v(0) = 1,...Ch. 15 - Solve the integrodifferential equation...Ch. 15 - Prob. 60P
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- 1. Find the Laplace transform of the given functions, where a and b are constants a) eat sinh bt b) eat cosh btarrow_forwardIn the circuit below, switch S has been closed for a long time, and opens at t=0 . Usethe Laplace transform method to compute Vc(t) for t ˃0.arrow_forwardThe switch was open for a long time but closed at t=0 Determine: (a) i(0 ), v(0 ), (b) di(0 ) dt, dv(0 ) dt, (c) i(infinity ), v(infinity).Apply Laplace transform to the given RLC circuit to solve differential equations with initial conditions. Please in typing formatarrow_forward
- Using the Laplace transform, i for t>Ofind it. vc(0-) = 3V, i(0-) = 0arrow_forwardSuppose for the circuit shown, Idc=24 mA, R=625 Ω, L=25 mH, and C=25 nF. There is no energy stored in the circuit when the switch opens at t=0. 1. Find V(s), the Laplace transform of v(t). 2. Find v(t) by finding the inverse transform of the partial fraction expansion of V(s).arrow_forwardSolve the following differential equations by using Laplace transform method. a) y'' +2y' + y = 4e−t where y(0)= 2 y'(0)= 4 .arrow_forward
- In the circuit given on the side; Since is=1,5e−2tu(t) A and iL(0)=1A, find ix(t) by the Laplace transform method. Some Laplace transform pairs are other users.arrow_forwardDetermine the inverse laplace transform of the following: a. 1/[(s-2)^2 + 9] b. s(s^2 - 9)/(s^2 +9)^2arrow_forwardGiven the following circuit, find i(t) at t>0. (R=3 ohm, L=1H, C=0.5F, is=2e^-3t). Solve without using Laplace Transform.arrow_forward
- Prove that the differential equation below can be converted to Laplace Transform; with initial conditions being zeros. d^3y/dt^3 + 10d^2y/dt^2+20dy/dt= 8u(t)arrow_forwardthe inverse laplace transform for the following function: X(s) = (5s + 2)/( s2 + (5/2)s + 1 ) i need detailed steps on how to complete the inverse transform of the above problem. if you could also include notes on how to procede on future problems will be greatly appreciated.arrow_forwardFind the laplace transform of the following equation. 1.f(t)=u(t)-u(t-1) 2.f(t)=cos5t.u(-t) 3.f(t)=sint.u(t).etarrow_forward
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